Prior Art
There are numerous publications and patents regarding information compression which lay out methods by which functions[23] which effectively model the signal and which ineffectively model the noise[37] are used to encode (fit the function[25]) the signal and then later decode (expand the function [27]) it. No mention has been found, however, regards using this as a means to remove noise from images or, in particular, to remove noise from medical images[2].
Utilizing the most recently acquired image and one or more previously acquired images for
  signal  noise[38] enhancement has been described using frame averaging. This is particularly to be found in medical ultrasound[6] applications. No mention has been found that this frame averaging is a special case of a more general formulation which would provide much more powerful signal enhancement.
Frame averaging is typically performed for the individual pixels in the reduced noise image[39]. The noise reduction is approximately √{square root over (N)} where N is the number of images in the average, i.e. the number of pixels used for each averaged pixel in the reduced noise image. Noise reduction in this context is expressed as the ratio of the noise values of the original and noise reduced image. Since N is typically 2, the noise reduction produced by frame averaging is typically √{square root over (2)}≅1.414. Note that the function which is used is one-dimensional.
The information compression literature and methods typically involve one or two-dimensional functions, e.g. the discrete cosine transform, and typically utilize 64 points at a time or less. The claimed method utilizes functions with one or more dimensions. In so doing the number of points included in each fit is potentially much higher than that typically used for either frame averaging or image compression. Monte Carlo simulations of the claimed method have shown that the resultant noise reduction is correspondingly increased to approximately
            N      -      df      -      1        2where N is the number of pixels in a pixel block[14], i.e. the number of pixels used for each fit, and df is the number of parameters[24] in the function.
In one test, N, the number of pixels in the pixel block was 512 (16×16×2) and df was 72 (6×6×2), producing estimated noise reduction of approximately
                    512        -        73              2    =                    439            2        ≅          110        ≅          10.5      .      In another test 4-parameter basis functions were used along each of the 3 axes, for a total of 64 parameters, and 10 observations along each axis, for a total of 1000. The measured noise reduction achieved in that test was approximately 20. This is more than ½ of the theoretical ideal enhancement achievable with averaging, namely √{square root over (1000−64−1)}≅30.5.
Note that each image is a 2-dimensional object and that a sequence of images forms a 3-dimensional object. Thus the “curve”fitting and subsequent function expansion may be carried out in 1, 2, or 3 dimensions, readily providing the contribution of an enormous number of observations to the estimation of each parameter with greater noise reduction than was previously achievable.
Specific considerations for use in fluoroscopy[5] during medical procedures[7]: There is a wide variety of clinical procedures which require acquisition of numerous lengthy fluoroscope image sequences. For example, neuroradiologic intervention is a common treatment of vascular lesions and neoplasms of the head and neck which requires extensive use of fluoroscopy, i.e. serial X-ray imaging. Typical fluoroscopy times are on the order of 60 minutes [Kuwayama et. al., 1994]. At a full 30 frames per second, 60 minutes of fluoroscopy represents 108,000 X-ray images, a very significant dosage to the patient. Even for the practitioner, scattered X-rays from one hour of fluoroscopy produce as much as ⅕ the acceptable whole body yearly dose [Giblin et. al., 1996].
This exposure can be reduced by 75% or more by pulsed fluoroscopy, i.e. reduced frame rate imaging [Bushong, 1994]. Even with 90% reduction, the equivalent 10,800 X-ray images represents considerable exposure, not only for the patient, but for radiologic personnel who perform such procedures 100's of times each year.
Reflective of these large X-ray dosages, fluoroscopy during endo-vascular procedures of the head and neck carry significant risks, e.g. skin reactions [Huda, 1994, Carstens et. al., 1996]. This coupled with progressively diminishing acceptable exposure values [Bushong, 1994] has led to considerable and persistent interest in studying X-ray exposure during neurovascular interventions [Chopp et. al., 1980, Plunkett et. al., 1986′, Berthelson et. al., 1991, Hughes et. al., 1994], [Marshall, Faulkner, 1995, Bergeron et. al., 1994]. A variety of strategies have been devised to minimize X-ray exposure both for the patient and radiologic personnel including proper room design and body shielding [Bales, Greening, 1991], use of filters to protect the eyes [Chakeres, Wiatrowski, 1984] and to reduce over-all X-ray exposure [Katsuda et. al., 1996], sophisticated collimation techniques [Rudin et. al., 1996], the above mentioned pulsed fluoroscopy [Bushong, 1994] to reduce the number of images per second, and the ongoing development of more sensitive cameras which enables high resolution images with reduced X-ray flux. Note that reduced X-ray flux means reduced X-ray intensity means reduced numbers of X-ray photons.
The need is to reduce X-ray dose to patient and radiologic personnel during fluoroscopic procedures while maintaining acceptable quality images. The claimed method and apparatus are unique and powerful. They enable generation of acceptable quality images with a fraction of the X-ray intensity which would otherwise be required. Reducing the X-ray intensity correspondingly reduces the X-ray dose to which both patient and radiologic personnel are exposed, irregardless of other dose reduction techniques which are in use.
The technical problem which must be solved arises because reduced X-ray flux produces increased random noise[42] in the image [Reichman, Astrand, 1979] as well as image darkening and reduced contrast, i.e. the X-ray intensity, the number of X-ray photons/image, is positively correlated with the
  signal  noise(Reichman, Astrand, 1979). This gives rise to conflicting requirements: maximizing the X-ray intensity improves the
      signal    noise    ,yet it also maximizes the X-ray dosage to which the patient and radiologic personnel are exposed.
To summarize the background the proposed method and apparatus enable considerably greater noise reduction in images than had previously been available. It is highly effective at attenuating random noise, which is a major contaminant of X-ray images acquired with low doseage. Because the claimed method can attenuate random and other types of noise, it is effective at recovering image quality when contaminated due to reduced doseage. Even though there are a wide variety of techniques already in place to reduce X-ray doseage during medical procedures which utilize fluoroscopy, there continues to be a significant risk of overexposure leading to morbidity for both the patient and the medical personnel. The claimed method and apparatus provide a means by which the doseage can be routinely reduced by a factor of 3 or more, dramatically reducing the risks.